Space
Are there more possible chess games than atoms in the universe?
The short answer
Yes. The number of possible chess games is estimated at around 10^120, known as the Shannon number. The observable universe contains roughly 10^80 atoms. Chess outruns it by about forty orders of magnitude.
Claude Shannon worked the estimate out in 1950, in a paper about whether a machine could be taught to play. His arithmetic was deliberately rough: assume a game runs about 40 moves per side, and assume roughly 30 legal moves available at each turn. Thirty options, taken eighty times over, gives about 10^120.
The atom count is the other kind of estimate — physics rather than combinatorics — and it lands near 10^80. The gap between the two numbers is not a near thing. It is 10^40, which is to say the chess number is a trillion trillion trillion times larger.
None of this makes chess unsolvable in principle, and it isn't a claim about the number of positions, which is far smaller. It is a claim about distinct games. A board with 32 pieces on 64 squares generates more histories than the universe has parts.
Sources
- Which is greater? The number of atoms in the universe or the number of chess moves?National Museums Liverpool
- Shannon numberWikipedia